IE does not get more specific than [object] in any case, so this is
unrelated to sarissa or XSLT.

alert(resultDocument.xml) in IE shows the xml content of the document,
in firefox shows undefined.

You should read the API documentation; the .xml property has been
removed as there was no way to support itin browsers other than IE and
Moz. Instead, you can use the XMLSerializer object or the
Sarissa.serialize utility method.

The same is the case for all the usual properties that the MS dom exposes, text
etc. how do I have to get ahold of those properties?

Although sarissa begun as a library to emulate IE extentions to the DOM,
it changed along the way to support more popular and non-IE centric
extentions. Check out the documentation.